The classic example of the not-well-understood rapid change of tectonic plate motion is the increase and then decrease of the convergence rate between the Nazca and South America plates during the past 25–20 m.y. that coincided with the growth of the Andes Mountains. Currently, the decrease in convergence rate is explained either by the increasing load of the Andes or by the appearance of flat slab segments beneath South America. Here, we present an alternative view based on a thermomechanical self-consistent (gravity driven) model of Nazca plate subduction. We explain the changes in the convergence rate as a natural consequence of the Nazca plate penetration into the transition zone and lower mantle after long-term oblique subduction of the Farallon plate. The model is consistent with seismic tomographic images of the Nazca plate beneath South America. Our model also shows that the presence of the Andes does not significantly affect the convergence rate between the Nazca and South America plates.